Unlike vector data, pixels in raster datasets do not inherently belong to a given feature. The pixels simply have a value. So it's not so much that the entire raster dataset is one big clump, it's that all of pixels have the same value. You could assign each "clump" it's own value. While the resulting "zonal raster" could be used as an input for a number of functions (e.g., Zonal Geometry), I believe that accurately reclassifying the pixels in this way would be very difficult and time consuming.
I would consider Focal Statistics, which eliminates small variations in raster data, so that only the largest contiguous blocks remain. When using a majority statistic type, each pixel will be assigned the value that is most prevalent within a certain proximity of that pixel. So, if the user selects a 5x5 rectangular neighborhood, each pixel will receieve the value that is most prevalent in the 25 pixels closest to it. Because of this, small areas of isolated wetland surrounded by no wetland would be reclassified as "no wetland". While it may be difficult to eliminate clumps that fall below your 5 acre threshold exactly, this is a very effective tool to achieve what you're generally looking for. Try experimenting with different neighborhood sizes to see how the results vary.
You may also try converting the raster to polygon, calculting the size of the different polygons, and then doing a select by attribute to identify contiguous wetlands over 5 acres.